Porous Convection in the Discrete Exterior Calculus with Geometric Multigrid
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912541261692928 |
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| author | Morris, Luke Rauta, George Carlson, Kevin Fairbanks, James |
| author_facet | Morris, Luke Rauta, George Carlson, Kevin Fairbanks, James |
| contents | The discrete exterior calculus (DEC) defines a family of discretized differential operators which preserve certain desirable properties from the exterior calculus. We formulate and solve the porous convection equations in the DEC via the Decapodes.jl embedded domain-specific language (eDSL) for multiphysics problems discretized via CombinatorialSpaces.jl. CombinatorialSpaces.jl is an open-source Julia library which implements the DEC over simplicial complexes, and now offers a geometric multigrid solver over maps between subdivided simplicial complexes. We demonstrate numerical results of multigrid solvers for the Poisson problem and porous convection problem, both as a standalone solver and as a preconditioner for open-source Julia iterative methods libraries. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_12501 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Porous Convection in the Discrete Exterior Calculus with Geometric Multigrid Morris, Luke Rauta, George Carlson, Kevin Fairbanks, James Computational Engineering, Finance, and Science The discrete exterior calculus (DEC) defines a family of discretized differential operators which preserve certain desirable properties from the exterior calculus. We formulate and solve the porous convection equations in the DEC via the Decapodes.jl embedded domain-specific language (eDSL) for multiphysics problems discretized via CombinatorialSpaces.jl. CombinatorialSpaces.jl is an open-source Julia library which implements the DEC over simplicial complexes, and now offers a geometric multigrid solver over maps between subdivided simplicial complexes. We demonstrate numerical results of multigrid solvers for the Poisson problem and porous convection problem, both as a standalone solver and as a preconditioner for open-source Julia iterative methods libraries. |
| title | Porous Convection in the Discrete Exterior Calculus with Geometric Multigrid |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2508.12501 |